Question

Use the image to answer the question.

A coordinate plane of 4 quadrants shows x and y axes ranging from negative 3 to 3 in increments of 1. A line with arrows at each end intercepts two plotted points, A and B. Point A is plotted at left parenthesis negative 2 comma 0 right parenthesis. Point B is plotted at left parenthesis 0 comma negative 1 right parenthesis. The coordinates are not labeled.

Which of the following is the equation of the line on the graph?

(1 point)
Responses

y=12x−1
y equals Start Fraction 1 over 2 End Fraction x minus 1

y=−2x−1
y equals negative 2 x minus 1

y=−12x−2
y equals negative Start Fraction 1 over 2 End Fraction x minus 2

y=−12x−1
y equals negative Start Fraction 1 over 2 End Fraction x minus 1
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Answer 1

To find the equation of the line that passes through points A \((-2, 0)\) and B \((0, -1)\), we can follow these steps:

1. **Calculate the slope (m)**: The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in the values:

\(
m = \frac{-1 - 0}{0 - (-2)} = \frac{-1}{2} = -\frac{1}{2}
\)

2. **Use the point-slope form to write the equation of the line**: The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

Using point B \((0, -1)\) and the slope \(-\frac{1}{2}\):

\[
y - (-1) = -\frac{1}{2}(x - 0)
\]

This simplifies to:

\[
y + 1 = -\frac{1}{2}x
\]
\[
y = -\frac{1}{2}x - 1
\]

3. **Identify the answer choice**: The equation we derived is:
\[
y = -\frac{1}{2}x - 1
\]

Thus, the correct choice from your provided options is:

**y = −\frac{1}{2}x − 1**.